Channel estimation is challenging for hybrid millimeter wave (mmWave) large-scale antenna arrays which are promising in 5G/B5G applications. The challenges are associated with angular resolution losses resulting from hybrid front-ends, beam squinting, and susceptibility to the receiver noises. Based on tensor signal processing, this paper presents a novel multi-dimensional approach to channel parameter estimation with large-scale mmWave hybrid uniform circular cylindrical arrays (UCyAs) which are compact in size and immune to mutual coupling but known to suffer from infinite-dimensional array responses and intractability. We design a new resolution-preserving hybrid beamformer and a low-complexity beam squinting suppression method, and reveal the existence of shift-invariance relations in the tensor models of received array signals at the UCyA. Exploiting these relations, we propose a new tensor-based subspace estimation algorithm to suppress the receiver noises in all dimensions (time, frequency, and space). The algorithm can accurately estimate the channel parameters from both coherent and incoherent signals. Corroborated by the Cram{e}r-Rao lower bound (CRLB), simulation results show that the proposed algorithm is able to achieve substantially higher estimation accuracy than existing matrix-based techniques, with a comparable computational complexity.
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